The seminal paper on best subset selection using MIO [1]} proposed two primal formulations for sparse regression. Both of these formulations use binary variables to encode the support of the coefficients, one using big-M constraints, and the other using type-1 specially ordered sets (SOS-1). Because the system identification problem is coordinate separable, we can fit each dimension independently, resulting in \(d\)  smaller subproblems which can be solved directly using these techniques.
